This application relates to image processing methods and systems, including methods and systems to segment objects in images.
Many image analysis and filtering techniques require a notion of how likely two neighboring pixels/voxels are to belong to the same object. Examples of this type of algorithm include anisotropic diffusion, Dirichlet filtering, region growing, graph cuts, normalized cuts, intelligent scissors/live-wire, the isoperimetric algorithm and the recently developed random walker algorithm. As first introduced by Perona and Malik, and later reinforced, the typical function for assigning diffusion constants (i.e., graph weights) is
                                          w            ij                    =                      exp            ⁢                                          (                                                                                                                        z                        i                                            -                                              z                        j                                                                                                  2                                )                                            σ                2                                                    ,                            Eq        .                                  ⁢                  (          1          )                    where wij, is the weight between pixels i and j, zi is a vector representing the value at pixel i (e.g., intensity, color) and σ is a free parameter.
Unfortunately, a method of computation for the norm in Eq. (1) remains undefined. When zi is a one-dimensional intensity, this problem is not an issue, since most standard norms default to a simple subtraction between the intensities. However, multi-channel images are common in the medical, industrial and graphics communities. Such images may arise as a result of the registration of multiple images taken from different time points, multiple images taken with different contrast agents and/or pulse sequences, “hyperspectral” imagery taken from radar and, perhaps most commonly, color images (in which case the zi vector typically represents the RGB values at pixel i.
For lack of a more principled choice, the norm in Eq. (1) is typically taken as the Euclidean, L2, norm or the L∞ norm. However, it has been widely noted how inadequate the Euclidean norm is in almost all spaces (e.g., color images).
The present methods of image processing and determining weighting coefficients for pixels in an image do not yield completely satisfactory results, particularly when processing color images. Accordingly, new and improved methods and systems for processing images to segment objects and to determine weighting coefficients are needed.